Presently commercially available echographic systems obtain information from the surrounding means and from human body, using elastic waves at ultrasonic frequency. To this end, the echographic probes generally use capacitive ultrasonic transducers, in particular obtained by means of silicon micromachining, capable to generate and detect ultrasonic waves, through which an ultrasonic imaging process (image generation) is carried out.
Capacitive transducers, constituted of two faced electrode (one of which is fixed and the other is movable) which are spaced apart by a cavity, are based on the electrostatic attraction force that is present whenever a charge amount is accumulated on the same electrodes by applying a potential difference. In order to obtain transduction linearity and efficiency a (biasing) dc voltage is usually applied to which a (signal) ac voltage is added.
In general, transmission transduction efficiency, i.e. the ratio of the transmitted acoustic pressure (proportional to the relative movement between the electrodes) to the applied ac electric voltage, increases with the increase of the biasing dc voltage and of the accumulated charge, i.e. it increases with the increase of the electric field present within the cavity.
In general, the reception transduction efficiency, i.e. the ratio of the transducer output voltage or current to the pressure incident on the transducer surface, also increases with the increase of the biasing dc voltage.
However, the open circuit reception efficiency (i.e. ideal voltage detection) is directly proportional to the biasing voltage and to the relative movement between the electrodes, while the short circuit reception efficiency (i.e. ideal current detection) is directly proportional to the static charge accumulated by means of the biasing voltage (that hence depends on the capacitance) and to the relative speed between the electrodes.
FIG. 1 shows the classical lumped parameter model of an electro-mechanical transducer. For a membrane capacitive transducer (such as a capacitive ultrasonic transducer), the mechanical behaviour may be approximated, in absence of losses and for frequencies close to the natural vibration first mode resonance frequency fris, as the Cm-Lm series, where Cm represents the membrane “compliance” and Lm represents the membrane “mass”.
These two quantities are proportional to the geometrical parameters (thickness t and side dimensions lx and ly), and to the properties of the materials of which the membrane is constituted (density ρ and Young modulus Ex) according to the following formulas:
                              C          m                =                              1            k                    ∝                                    E              x                        ·                                                            l                  x                                ·                                  l                  y                                            t                                                          [        1        ]            
where k is the stiffness constant of the equivalent spring, andLm∝ρ·lx·ly·t  [2].
Transformation factor φ depends on the capacitance value C0 of the transducer to which the only biasing voltage is applied, on the applied dc biasing voltage VDC, and on the distance dgap between the electrodes, according to the following formula:
                    ϕ        =                              C            0                    ⁢                                    V              DC                                      d              gap                                                          [        3        ]            
The collapse voltage Vcol, representing the maximum limit of biasing dc voltage VDC applicable to the transducer without collapse of the upper electrode on the lower one, is limited by the membrane compliance Cm: the more the membrane is stiff, the higher is the applicable dc voltage. In general, the collapse voltage Vcol is, for flexural capacitive transducers, equal to:
                              V          col                =                  α          ·                                                    d                gap                3                                                              C                  m                                ⁢                                  ɛ                  0                                                                                        [        4        ]            
with α that is constant and depending on how the flexural structure is constrained.
In order to increase the collapse voltage Vcol it is hence needed to decrease the membrane compliance Cm.
The increase of the collapse voltage Vcol (i.e. of the maximum applicable dc voltage VDC—max) entails the increase of the transformation factor φ, on which the transmission and reception efficiencies directly depend. The transformation factor is maximum when VDC=Vcol, and it is equal to:
                              ϕ          max                =                  α          ·          S          ·                                                    ɛ                0                                                              C                  m                                ⁢                                  d                  gap                                                                                        [        5        ]            
where S is the membrane area.
Thus, in order to increase the transduction efficiencies, it is needed a decrease of the membrane compliance Cm and a decrease of the electrode distance dgap.
FIG. 2 shows a sectional view (FIG. 2a) and a plan view (FIG. 2b) of an ultrasonic capacitive transducer. The vibrating structure is a plate 1 (usually made through a transparent membrane, as shown in FIG. 2b), provided with an electrode 15, that is constrained to a stiff substrate 2, in turn provided with an electrode 6, by means of an array of columns 3 arranged in an ordered manner (in the case of FIG. 2 it is a square grid of columns 3). Both electrodes 15 and 6 (represented in FIG. 2a with continuous lines), between which cavities 4 are interposed, are protected by a respective film 7 and 8 of insulating material. This film serves for preventing, in case of collapse of the membrane 1 on the substrate 2, the electrodes 15 and 6 from short-circuiting.
For reasons of efficiency, each insulating film 7 and 8 should be as thin as possible. In fact, the space between the two electrodes 15 and 6 is partly occupied by the insulating films 7 and 8. The capacitance between the two electrodes 15 and 6 may be hence seen as series of three capacities, only one of which is variable, thus constituting the active capacitance in the electromechanical operation, while the other two ones are due to the presence of the insulating dielectric material and they do not contribute to transduction (for this reason the series of these two ones is called parasitic series capacitance). The active capacitance is the one that varies under a flexural deformation of the membrane 1 and hence under the variation of the distance dgap between the electrodes 15 and 6. When a potential difference is applied at the ends of this series of capacities, it distributes between the active capacitance and the parasitic series one due to the protection films. Only the voltage across the active capacitance is responsible for the mechanical actuation of the membrane 1. For this reason it is convenient that the insulating material films 7 and 8 are as thin as possible.
Finally, the structure is covered by an insulating material film 9. This structure, also known as MAMMUT, has a natural vibration mode wherein all the cells delimited by four columns 3 vibrating with the same phase. The frequency of this mode (that will be called resonance frequency fris from now on) is determined by the geometric characteristics (thicknesses of the membrane 1, distance and size of the columns 3) and by the properties of the materials. The vibrational behaviour may, for frequencies close to the resonance frequency fris, be modelled by a lumped-parameter model as a system mass-spring (Cm-Lm), as previously shown with reference to FIG. 1.
However, conventional ultrasonic transducers suffer from some limitations.
First of all, the transmission efficiency is equal to the ratio of the transmitted pressure to the applied ac voltage. In order to emit a certain pressure, the membrane must be able to vibrate with a sufficient amplitude along the propagation direction. The extent of this movement is connected to the generated pressure (to a first approximation) through the characteristic acoustic impedance Za of the fluid, defined as the ratio of the pressure P to the velocity v of the fluid particles for plane wave propagation:
                              Z          a                =                              P            v                    .                                    [        6        ]            
Points over the transducer surface will have a velocity v equal to:
                    v        =                  β          ·                      P                          Z              a                                                          [        7        ]            
wherein β is constant (ranging from 0 to some units) and depending on the position of each single point. Movement u if such points is related to velocity and vibration frequency f:
                    u        =                  v                      2            ⁢            π            ⁢                                                  ⁢            f                                              [        8        ]            
Therefore, a decrease of the distance dgap between the electrodes 15 and 6, on the one hand, increases the electrostatic pressure acting on the movable membrane 1, but, on the other hand, limits the maximum amplitude of the membrane movement, and hence the maximum transmitted pressure P.
Moreover, the flexural capacitive transducers are usually used in applications wherein a large bandwidth is required. This is obtained by designing the flexural structures so that their mechanical impedance Zm have module lower than or comparable to the acoustic impedance Za of the fluid wherein it is desired to generate acoustic waves for an extended frequency range (approximately the one of the transmission band at −6 dB).
Therefore, since the mechanical impedance of a flexural structure is equal to:
                                          Z            m                    =                                    j              ⁢                                                          ⁢              ω              ⁢                                                          ⁢                              L                m                                      +                          1                              j                ⁢                                                                  ⁢                ω                ⁢                                                                  ⁢                                  C                  m                                                                    ,                            [        9        ]            
by decreasing the structure compliance Cm, the module of the mechanical impedance Zm increases with a consequent reduction of the bandwidth. In other words, a decrease of the flexural structure compliance Cm increases the electro-mechanical transformation factor φ, and hence the transmission and reception transduction efficiency, to the detriment of the transducer bandwidth.